Abstract: In the paper，we construct a kind of M-bond multiwavelet base on slant transform and the relationship between Walsh transform and wavelet. The filter banks of these M-bond multiwavelets are conveniently generated by the fast algorithms of Slant transform, this method of designing the multiwaveleis filter banks is less oneness and complexity than the traditional method .We apply this kind of M-bond multiwavelets to image denoising and image compressing, the result is more excellent than the traditional DWT and the result of the image denoising is better than the M-bond Multiwavelet which bring forward in [6].

Key words: Walsh transform, Slant transform, M-bond multiwavelet, image denoising, image compressing

摘要： 本文根据Walsh变换与小波之间的联系，在斜变换的基础上提出了一种新的多进制多小波设计思想，改变了传统小波变换中滤波器设计方法的单一性和推导的复杂性，该滤波器组利用斜变换的快速算法生成简单方便。将该方法应用于图像去噪和图像压缩的实验中，实验结果证明该方法的去噪效果和压缩效果要优于传统的DWT，并且去噪效果还要优于文献[6]中提出的多进制多小波。

关键词: Walsh变换, 斜变换, 多进制多小波, 图像去噪, 图像压缩